Delete part of an imported obj model in Blender?
Is the meshed separated in group for OBJ file?

Try to use Split by Group in importing OBJ file:



In that way, the object can be imported separately if the OBJ use group for objects.

Just delete the object by X 

If the Object is still joined

Enter edit mode and deselect all vertices alt+A, and hover on the main structure and press L for linked mesh. Revert your selected by Ctrl+I and delete those vertices.